Find the equation of the family of curves whose slope at any point (x, y) is -4e-2ª sin 2x. Find the equation of the member which passes through (0, 1).

Q: Find an equation of the line tangent to the curve defined by z2 + 6ry +y = 32 at the point (2, 2).

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Q: Find an equation of the tangent line to the curve at the given point. 6. y =x² – 3x +1, (2, –1)

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Q: Find the equation of the curve that passes through the point (7,5) if its slope is given by dy 3D 8х…

A: We have to find

Q: Find an equation of the tangent line to the graph of the equation  x + y − ex − y = 3 at the point…

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Q: Find an equation for the tangent to the 6x at the point (1, 3). x2 + 1 curve y =

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Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: The slope of the tangent line to the parabola y = 2x + 5x + 7 at the point (- 4, 19) is: The…

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Q: Find an equation of the line tangent to the curve defined by x2 + 6xy + y 32 at the point (2, 2).…

A: v

Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: Find the equation of the curve that passes through the point (3,6) if its slope is given by dy = 6x…

A: Note: As per company policy we are supposed to solve only one question. So, kindly re-post the other…

Q: Find the equation of the curve that passes through the point (6, 6) if its slope is given by dy = 7x…

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Q: Find the equation of the line tangent to the graph of y = 3x cos x at the point (π, −3π).

A: Given Data: Equation: y=3xcosx Point: (x1, y1)=(π, −3π) The derivative of the given equation of…

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: Find the equation of the curve that passes through the point (8, 8) if its slope given by dy 3D 7х —…

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Q: Find the slope of the line tangent to the graph of y = cos 3xat x = 13π/6.

A: The slope (m)  of the line tangent to the graph y=f(x) at point (x1,y1) is given by:

Q: Find the equation of the tangent line to the curve at the given point.

A: To find the tangent at the given point on the curve, using derivatives

Q: Find the equation of the line tangent to the curve y = cos(2x) at the point where 3

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Q: Find the equation of the curve at every point of which the tangent line has a slope of (1+y^2)/2xy…

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Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

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Q: At what point on the interval (0, 7/2) does the tangent line to the curve = 3x + V3 cos x – sinx…

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Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

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Q: Find the equation of the tangent line to the graph of 3x- xy + y - 9 = 0 at the point (2, -3).

A: The graph of 3x3-x2y+y3-9=0 at the point 2,-3

Q: Find the lengths of the curves y = sin -1x - √(1 - x2), 0≤ x ≤ 3/4

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Q: At the given point, find the line that is tangent to the curve. 5x3y - n cos y = 6t, tangent at (1,…

A: 5x2y-πcosy=6π=ddx(5x2y-πcosy)=ddx(6π)=10xy+5x2y'+πy'siny=0=(5x2+πsiny)y'=-10xy y'=-10xy5x2+πsiny…

Q: Find the equation of the tangent line to the graph of x^2 * y^2 + 6xy =1512 at the point (-7,6)

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Q: Find an equation of the line tangent to the graph of y sin x – 3y = 4 at the point %3D (, 4) .

A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

Q: Find the equation of the line that is tangent to the curve y = 4x cos x at the point (7, –4t). The…

A: we have to find the equation of tangent

Q: Find an equation of the tangent line to the curve at the given point. x2 (4, 16) y

A: Given ex2-y=x2y To find equation of tangent at the point 4,16

Q: Find the slope of the Curve r=-I+Sine atthe points 8=0,T-

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Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

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Q: Find the equation of the curve that passes through the point (7,3) if its slope is given by dy = 7x…

A: As per our company's policy, we can solve first question only. Please repost other question…

Q: Find the slope of the line tangent to the graph of y = sin 2xat x = 5π/4.

A: Slope of the line tangent to the graph of y = sin 2x at x = 5π/4. y(x) = sin 2x y'(x) = (sin 2x)' =…

Q: find the inflection point to the right of y-axis of the curve defined by the equation, y=x^2/2 +…

A: Given problem :- find the inflection point to the right of y-axis of the curve defined by the…

Q: find an equation for the tangent line to the graph of y=(5-2x)^2 at (3,1).

A: Explanation of the answer is as follows

Q: Find an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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Q: Find an equation of the tangent line to the graph at the given point. x2y2 − 9x2 − 4y2 = 0,…

A: Given that, x2y2 - 9x2 - 4y2 = 0 Points are :  (-4, 23) We have to find the tangant line to the…

Q: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

Q: Find the equation of the curve that passes through the point (8, 4) if its slope is given by dy = 5x…

A: Using variable separable form of Differential equation.

Q: Find the equation of the line that is tangent to the curve y =-3e* at x = In 2. %3D

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Q: The equation of the tangent to the curve y = x – 3x² – 2x + 2 at the point where the curve cuts the…

A: We have to find  the equation of tangent in the form of y=mx+c.

Q: Find the equation of the curve that passes through the point (3, 8) if its slope is given by dy 3x –…

A: We have to find equation of curve

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

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Q: Find the equation of the line tangent to the curve y=x+cosx at the point (0,1)

A: Given, curve and point

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: Find the equation of one of the tangent lines to the circle x2 + y2 = 52 that pass through the point…

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Q: Find the equation of the line tangent to y = sin(x) going through 4

A: Given, y=sinx                 ...(1) At x=π4 Put x=π4 in equation (1) y=sinπ4y=22 Thus, the pointπ4,…

Q: The f '(x) of the given curve is equal to -4 y = sin 3x ||

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Q: The curve defined by the equation x^2+y^2=(2x^2+2y^2-x)^2 is called a cardioid. Find the equation of…

A: consider the given equation, x2+y2=2x2+2y2-x2 Use implicit differentiation method and differentiate…